Problem: $z=20i+26$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=26$ and $\text{Im}(z)=20$ (Choice B) B $\text{Re}(z)=26$ and $\text{Im}(z)=20i$ (Choice C) C $\text{Re}(z)=20i$ and $\text{Im}(z)=26$ (Choice D) D $\text{Re}(z)=20$ and $\text{Im}(z)=26$
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={20}i+{26}$ is of the form ${b}i+{a}$, where ${a}={26}$ and ${b}={20}$. Therefore: $\text{Re}(z)={a}={26}$. $\text{Im}(z)={b}={20}$. Summary $\text{Re}(z)={26}$ and $\text{Im}(z)={20}$.